Deconfined quantum criticality with internal supersymmetry

TL;DR

This paper extends the deconfined quantum critical point concept to systems with internal supersymmetry, proposing a supersymmetric DQCP with a non-linear sigma model and gauge theory description, connecting to conventional DQCP.

Contribution

It introduces the supersymmetric deconfined quantum critical point (sDQCP) framework for systems with internal supersymmetry, specifically using the $OSp(1|2)$ superalgebra.

Findings

Formulated a non-linear sigma model on the supersphere for sDQCP.

Developed a gauge theory to analyze dynamical properties.

Connected sDQCP to conventional DQCP by breaking supersymmetry.

Abstract

Deconfined quantum critical point (DQCP) describes direct, non-fine-tuned quantum phase transition between two ordered phases that break distinct and seemingly unrelated symmetries, providing a route to continuous phase transition beyond the conventional Ginzburg--Landau paradigm. In this work we extend the DQCP paradigm to systems with internal supersymmetry (SUSY), where the on-site Hilbert space furnishes a representation of a Lie superalgebra, and the Hamiltonian is invariant under the corresponding Lie supergroup. Focusing on the minimal supersymmetric generalization of spin $SU(2)$, namely $OSp(1|2)$, we propose a supersymmetric deconfined quantum critical point (sDQCP) between a phase that breaks internal $OSp(1|2)$ and a phase that instead breaks lattice rotation symmetry. We formulate a non-linear sigma model on the supersphere target space that captures the symmetry intertwinement characteristic of the sDQCP, and we further develop a gauge theory description to address its dynamical properties, including a heuristic argument for 3D XY critical behavior. Finally, we show that explicitly breaking $OSp(1|2)$ down to $SU(2)$ continuously connects our sDQCP to the conventional DQCP scenario.